In terms of an open source platform, Magento, OpenCart and PrestaShop are all fairly evenly matched in regard to security. osCommerce is probably the platform with the most active history of insecurity.

Look for providers that are PCI compliant. A lot of open source options will lack PCI compliance though. So, it may make sense to look at third party providers like Shopify, BigCommerce, or Magento Enterprise.

The developer in me tends to lean towards open source options that I can customize to my exact specifications. However, the realist, and the smart businessman, in me tell me not to try to re-invent the wheel and go with an established ecommerce provider.

I always suggest making a list of features you need (initially and in the future), then start looking at different systems to see which ones match the best. It also pays to set a software budget for initial purchase, cost and 3rd party addons (if needed), and any custom work that may need doing.

Obviously the more a shopping cart system does "out of the box" the better, so it's worth investing in the right software from the offset. Also worth noting software with a free to use licence sounds appealing intially but it can sometimes work out more expensive in the long run if you have to do a lot of customsation compared to a commercial system that needs little extra work,